Groups and Symmetries (U01409)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : PHY-4-GroupSym

This course provides an introduction to the theory of groups and their applications in physics. No previous knowledge of groups is required, but the applications build on classical and quantum mechanics. The topics covered are: finite group theory; representations of finite groups; Lie groups and their representations; applications in classical and quantum physics. This course makes intensive use of vector spaces and linear algebra. Tensors & Fields (PHY-3-TensFlds) and Lagrangian Dynamics (PHY-3-LagDyn) provide a useful background for the material presented in the course.

Entry Requirements

? Pre-requisites : At least 40 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 3 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
18/09/2007	10:00	11:00	Lecture Room 5326, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	10:00	10:50	KB
Lecture	Friday	10:00	10:50	KB

Summary of Intended Learning Outcomes

Upon successful completion of the course, it is expected that students will be able to:
1)understand the basic ideas of finite group theory
2)understand the representation theory of finite groups
3)understand the construction and use of character tables
4)understand the use of finite group theory in classical mechanics
5)understand the use of finite group theory in quantum mechanics
6)understand SO(2), SO(3), U(1) and SU(2) and their associated algebras
7)understand the use of these continuous groups in quantum mechanics
8)appreciate the role played by symmetries fundamental physics

In all the above the generic word "understand" is used to mean that the student must be able to use what he has learned to solve a range of unseen problems. The style and level of difficulty of these problems may be found from solving the examples provided in the course, and by the study of past exam papers. A more complete specification of the material included in the course may be found in the syllabus.